Simplify the following expression: $ n = \dfrac{1}{4} - \dfrac{2r}{-r - 3} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-r - 3}{-r - 3}$ $ \dfrac{1}{4} \times \dfrac{-r - 3}{-r - 3} = \dfrac{-r - 3}{-4r - 12} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{2r}{-r - 3} \times \dfrac{4}{4} = \dfrac{8r}{-4r - 12} $ Therefore $ n = \dfrac{-r - 3}{-4r - 12} - \dfrac{8r}{-4r - 12} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-r - 3 - 8r }{-4r - 12} $ Distribute the negative sign: $n = \dfrac{-r - 3 - 8r}{-4r - 12}$ $n = \dfrac{-9r - 3}{-4r - 12}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{9r + 3}{4r + 12}$